Question

Resistance of a wire is $R$ and cross-section area is $A$ now areas change to $N$ times. What will be the new resistance?

Answer 1

Step 1: Given:

Resistance: It is a measure of the opposition to the current flowing in an electrical circuit.

Given,

1. Resistance of a wire is $R$.
2. The cross-section area is $A$.
3. Areas change to $N$ time, i.e., $A_2=N·A$

Step 2: Formulas used

We know that,

$R=\frac{\rho L}{A}$

Where $\rho$ is the resistivity of the conductor, $L$ is its length and $A$ is its area.

Step 3: Calculate new resistance:

Initially, the resistance of the wire was,
$R_1=\frac{\rho L}{A}$

After the change in area, the volume remains the same.
$\begin{array}{ccc}& R_2=\frac{\rho L}{N·A}& \\ \therefore & R_2=\frac{R_1}{N}& \left[\because R_1=\frac{\rho L}{A}\right]\end{array}$

Hence, new resistance is will be $\frac{1}{N}$ times the initial resistance.